Liverpool missed the chance to go five points clear at the top of the Premier League table on
Saido Mane shot the Reds into the lead after 22 minutes but Michail Antonio leveled scored for the Hammers six minutes later.
Javier Hernandez and Aaron Cresswell came close to scoring in the opening 10 minutes as West Ham made the brighter start but it was the visitors who took the lead through a neat finish from Mane.
The Senegales forward turned his marker smartly inside the area before picking out the bottom corner for his third goal in as many games.
West Ham restored parity just six minutes later when Liverpool were caught napping from a slick free kick routine which allowed Antonio to escape Naby Keita and pick out the bottom far corner from inside the area.
In the second half, Liverpool continued to struggle to find rhythm although Mohamed Salah forced two brilliant saves from Fabianski six minutes after the restart and in the 56th minute.
Divock Origi missed a glorious chance to be the hero for Liverpool for a second time this season in additional time when he was one on one with Lukasz Fabianski – but he fired a tame shot straight at the goalkeeper.
Liverpool remain three points clear at the top of the table but Manchester City can return to the summit on Wednesday if they beat Everton- although the Reds will then have a game in hand.